Question

1. there are approximately 10^4 bacteria being studied in an experiment. with the introduction of a chemical, the bacteria multiply by a factor of 10^6. a second chemical reduces the population by a factor of 10^(-5). about how many bacteria remain? a. 1,000 bacteria b 10,000 bacteria c 100,000 bacteria d. 1,000,000 bacteria

Explanation:

Step1: Write the initial - bacteria population and factors

The initial number of bacteria is $10^{4}$. The first chemical makes the bacteria multiply by a factor of $10^{6}$, and the second chemical reduces the population by a factor of $10^{- 5}$.

Step2: Calculate the final number of bacteria

We use the rule of exponents $a^{m}\times a^{n}=a^{m + n}$. The final number of bacteria $N$ is given by $N = 10^{4}\times10^{6}\times10^{-5}$.
Combining the exponents using the rule $a^{m}\times a^{n}\times a^{p}=a^{m + n + p}$, we have $m = 4$, $n = 6$, and $p=-5$. Then $m + n + p=4 + 6+( - 5)=5$. So $N = 10^{5}=100000$.

Answer:

C. 100,000 bacteria